word problem

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Thu Jan 12, 2012 4:56 am

Of the people in a banquet, if 75% chose dissert, what percent chose coffee?
1). 60% of the people who chose dissert also chose coffee.
2). 90% of the people who chose coffee also chose dissert.

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 12, 2012 4:56 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Jan 12, 2012 4:10 pm

A - Total # of people who choose only Dessert
B - Total # of people who choose both Dessert and Coffee
C - Total # of people who choose only Coffee
D - Total # of people who choose nothing
X - Total # of people in the banquet

Given A+B = 0.75X, What is the value of B+C/(X)

1). 60% of the people who chose dissert also chose coffee.

B = 0.6X
A = 0.15X
C+D = 0.25X, Insufficient to find the value of B+C/(X)

2). 90% of the people who chose coffee also chose dissert.

0.9*(B+C) = B
Implies 9C = B,
Insufficient to find the value of B+C/(X)

From 1 and 2
B+C/(X) = (B + (B/9))/X = ((10/9)*0.15X)/X = (10/9)*0.15 Sufficient to answer IMO C

Anil Gandham
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